Low-coherence digital holography is confined to in-line holography because the interference fringes could be observed only when the angle between the object and reference light is small enough. Therefore, phase-shifting technique is usually employed. But it is not fit for dynamic analysis for demanding more than one hologram. However, the reconstructed image according to different sections of the object will be disturbed by the twin image and the out-of-focus section image by employing the traditional numerical reconstruction method for the analysis of one single in-line digital hologram. A numerical reconstruction method according to compressive sensing theory for the analysis of single low-coherence in-line digital hologram is proposed. By this method, the twin image and the coherent noise can be inhibited. The theory is presented in detail. Experimental research on light emitting diode-based digital holography is performed to demonstrate the feasibility and validity of the method.